A computational geometric approach for a novel multivariate process capability index

Process capability indices are useful tools, which provide common quantitative measures on manufacturing capability and production quality. The existing Multivariate Process Capability indices, Cpm, MCpm,[CpM, PV, LI], MCf & (sTpk} are proposed by different authors for different conditions and situations[1,2,3,4,5]. Many of the above multivariate process capability indices are based on the ratios of two areas or volumes for bivariate or in multivariate domain respectively. All above proposed indices assume the process to be normal and there by the indices are expressed in the form of ratios of areas of two ellipses or volume of two ellipsoids. When the process does not follow normal distribution the estimation of the index is difficult as the shape of the data distribution will be not known. The proposed MCsvdd index uses computational geometry and find out the convex hull of the process data to find the volume. Support Vector Data description helps to find the outliers.